Newton's law of motion Questions and Answers

a M m M 10 A rod of mass M m carries an insect of mass m at its bottom end and its top end is connected with a string which passes over a smooth pulley and the other end of the string is connected to a counter mass M Initially the insect is at rest Choose the correct option s m 11 12 As insect starts moving up relative to rod the acceleration of centre of mass of the system insect rod counter mass becomes non zero As insect starts moving up relative to rod tension in the string

Acceleration of blocks at given instant are a shown in the figure Coefficient of friction between 10kg block and ground is 0 1 There is no friction between 5kg blocks and ground Which of the following statements is are CORRECT F 20N A 5kg0000 10kg 0000000 5kg GER Force in spring A is 5N 0 o 2 In all other cases 0 0 Force in spring B is 15 N 4 Acceleration of block of mass 10 kg is 1 m s2 Spring A is in state of compression 5m s B 3m s

and larger radius and mass m is arranged with two massless strings and a block of mass Mas shown Both strings are wound tightly on the pulley The moment of inertia of the pulley about its central axis is 3mR 2 The system is released with both bodies at rest and both strings tight Let the acceleration of the centre of the pulley and the block be and A respectively Which of these options is are correct m M c A c 2A If M 2m the acceleration of the block is g 9 downwards If M m 2 the acceleration of the block is g 6 upwards

A double pulley of smaller radius R and larger radius 2R and mass m is arranged with two massless strings and a block of mass Mas shown Both strings are wound lightly on the pulley The moment of inertia of the pulley about its central axis is 3R 2 The system is released with both bodies at rest and both strings tight Let the acceleration of the centre of the pulley and the block be ac and respectively Which of these options is are correct e 24 11M 2m the acceleration of the block is g 9 downwards

b A pin jointed truss is loaded and supported as shown in Fig 2 b i Identify the members carrying zero force ii Find support reactions iii Find forces in all members by method of joints iv Find forces in the members CD CG and FG using method of section 80 KN 60 KN 00 B BOD 3 m 3 m

Multiple Ch Find the acceleration of the block in the given diagram 40 N Options 1 m s2 2 m s 4 kg 20 N

A flat car of mass m starts moving to the right due to a constant horizontal force F on a smooth ground Sand spills on the flat car from a stationary hopper The rate of loading of sand is constant and equal to m kg s The velocity of the flat car at time t is

32 System of Particles and Rotational Motion xample 13 Figure shows a pulley of mass m and radius r with two blocks of masses m and m attached with a light and unstretchable string Find the acceleration of the blocks tensions in the string and the force exerted by the pulley on the ceiling from which it is hanging Assume no slipping between the string and the wheel m g disc Pulley mig Mi m I R2 ein se chhota minus m m r T de

4 P Q and R are three identical blocks resting on s surface A force of 30 N is applied at one end as shown in the diagram below What are the tension T between blocks P and Q and T between blocks Q and R in the string P Q R 30 N Please also draw the diagram and show all forces acting on it Detailed explanation in step by step please

Two blocks A and B of mass 1 9 kg and 2 1 kg are suspended using an ideal massless pulley and string as shown Initially both blocks are at a height 40 cm from the ground The system is released from rest atr 0 Atz 1 0s the string suddenly breaks at the point it is attached to block B Atr 1 1s the velocity of the blocks A and B are vandv respectively and their height above the ground is hand he respectively Which of these options is are correct g 10 m s 0 D 20 40 cm v 0 5 m s downward V 1 5 ms downward h 25 cm h 5 cm

3 The resistance of a moving coil galvanometer is 195 Q and its full scale deflection current is 100 mA The resistance required to be connected to convert it into ammeter of range 4 ampere is 1 5 Q 2 10 Q 3 15 Q

Question No 16 A sphere of radius 5 cm and mass 4 kg rests on two point supports as shown such that the points A B and the centre of the sphere are in the same vertical plane Friction is absent The height difference between the supports and the centre of the sphere is shown in the figure The force in Newton acting on the sphere from the support A is g 10 ms 4 cm B 3 cm

In figure there are two particles A and B each of mass m A is connected to ceiling by a light inextensible thread OA and B is connected to A by light inextensible thread AB Initially line OB is vertical System is released from rest Initial acceleration of A and B are a and a respectively Find the value of 5a 2a2 530 37

Question No 69 Max Mark s 03 Multiple Choice Select 1 out of 4 options for the question below A car is moving with a constant speed on a straight road Find out the acceleration of car if the mass of the car is 500 kg and speed of car is 40 m s Options O 10 m s O 20 m s 15 m s

If a b and c are three forces of magnitudes 1 N 2 N and 3 N acting at a point such that the angle between any two is exactly 60 0 The magnitude of the resultant of the three forces is 5N O O 6N 4N

0 A block of mass m is kept in an elevator which starts moving downward with an acceleration a as shown in figure The block is observed by two observers A and B for a time intervalt The observer B finds that the work done by gravity is 1 J mgat 2 The observer B finds that work done by normal reaction Nis Nat A zero B Nat 2 The observer B finds that work done by pseudo force is A zero B ma t C ma t According to observer B the net work done on the block is mg t A mg 1 A ma t B mg t 2 B B ma t 2 C 1 c mgat 2 According to the observer A A the work done by gravity is zero C the work done by pseudo force is zero D all the above D mgat 2 DONO D None of these D mgat0 D mgat 2 B the work done by normal reaction is zero

the system shown in figure block A and C are placed on smooth floors and both have mass equal to my Blocks B and D are identical having mass my each oefficient of friction between A and B and that between C and D are both equal to H String and pulley are light A horizontal force F is applied on blcok C and is adually increased Find the maximum value of F tell it Fo so that all the four blocks move with same acceleration B A O 2 mg O 2 m g O 2 mg O 2 mg D m m 2m my m m 2m m my m 2m m m m 2m m F

The moment of inertia of a uniform circular disc about its diameter is 2kg m If its moment of inertia in kg m about an axis passing through its circumference and perpendicular to its circular face is 61 then value of I is

Q 5The cylinder P has diameter of 100 mm and weighs 200 N whereas the cylinder Q has diameter of 180 mm and weighs 500 N If the bottom width of the box is 180 mm with one side vertical and the other inclined at 60 determine the pressures at all the four points of contact TTTTTTTTTEK

and the string is tight Block 1 is moving on Two blocks of mass 1 kg each are moving with equal velocity 2 m s at the instant shown fixed frictionless horizontal surface Immediately after the velocity of block 1 is suddenly increased to 6 m s Assume that the string a pulley are ideal Which of these options is are correct g 10 m s O The string becomes tight again at t 0 4 s When the string becomes tight again it applies an impulse 2 kg m s directed upwards on block 2 O The velocity of block 1 immediately after the string becomes tight is 8 m s The heat generated when the string becomes tight is 4 Joules

90 Two particles are executing SHM of same frequency and of same amplitude along two closely separated straight line with their mean position at almost same position It is observed that maximum distance between the two is 2 times the amplitude Initially phase difference between the particle is A 1 90 3 45 1 X A x 0 x A 2 60 4 30

A cubical block A of mass m and a box B of same mass are lying on a horizontal surface as shown in the above figure The coefficient o kinetic friction between the block and horizontal surface is A while that between the box and surface is B Given that Att 0 the position is as shown in the figure and both are simultaneously given a velocity vo to the right The time after which block will collide with the right end of the box is B A 2 L 1 HB HA g OB 2 L 1 HB HA g Oc 4 L 1 HB HA 9 D 4 L 1 VHBMG

Il is dropped from some height on a floor with zero initial velocity At each collision with the floor the ball loses some speed ch of the following is the correct v t graph for this motion ne of impact of the ball with the ground is negligible Consider upward velocity as positive and downward velocity as negative

Sav A 60 kg boy carries a launcher loaded with a 15 kg ball The launcher is having negligible mass The boy can fire the ball v a relative speed of 10 m s The boy is skating on an ice rink can be assumed smooth with a velocity of 4 m s with respect ground The boy wants to fire the ball in such a way that his velocity turns through the largest possible angle Find this maximum angle in degrees swer Rate this ques

37 A air bubble of radius 1 cm in water has an upward acceleration of 9 8cms 2 The density of water is 1gmcm and water offers negligible drag force on the bubble The mass of the bubble is g 980 cm s A 4 15gm B 1 52gm C 4 51gm D 3 15gm

In figure Akshay Kumar of mass 80 kg man is on a ladder hanging from a balloon that has a total mass of 320 kg including the basket passenger Karina Kapoor The balloon and basket passenger Karina Kapoor is moving horizontally at 0 5 m s relative to the ground The man on the ladder begins to climb at 2 5 m s relative to the ladder A The balloon moves with a speed of 50 2 cm s B The velocity of the balloon makes an angle of 45 with the horizontal C If the man then stops climbing the speed of the balloon is 50 cm s D None 770931

A block A of mass 0 2 kg and a block B of mass 0 5 kg are placed on smooth horizontal surface at a distance of 42 m as shown below A force of 6 N is applied on each block to bring them closer 0 5 kg 0 2 kg 6 N A Choose the correct statement s A K 42 m Smooth horizontal surface One More Correct Answer s Acceleration of block A is 20 m s2 B Acceleration of block B is 12 m s Time n at which they meet with each other is 25 6 N The ratio of distance travelled by block A to block B to meet is 5 2 4 27

In the figure shown below the mass of block A B and C are 7kg 4kg and 3 kg respectively Coefficient of friction betwe friction between B and C is 0 3 There is no friction between ground and A Force F of 70N is applied on block B rightwan Find the direction of friction force on block A and C respectively 44 C C B F

A machine gun has a mass of 15 kg It fires 100 gram bullets at the rate of 40 bullets per minute at a speed of 600 m s What force is required to keep the machine gun in position a 40 N b 50 N d 57 N

Consider the shown arrangement of three blocks A B and C Mass of the each block is 1 kg The coefficient of friction between any twa blocks is 0 2 There is no friction between the block C and the ground Find the minimum value F in N for which sliding occurs at all the surfaces A B C Smooth ground F

on and ode A body of mass 4 kg is placed on a smooth inclined plane of inclination 60 The horizontal force to be applied to make the body move up the plane with an acceleration 2 m s is g 10 m s 068 N 0 72 N O 84 N O 90 N

If a particle have velocity and acceleration given 32 47 ms 4i 33 ms 2 respectively What would be the rate of change of spe at that instant A4 8 ms 2 B 5 ms 2 c 3 ms 2 DD 4 ms 2

Two blocks of masses m and M are placed on a horizontal frictionless table connected by light spring Mass M is pulled to the right with a force F if the acceleration of the mas sm is a then the acceleration of mass Mw ill be

Question 10 A block of mass 3kg is connected with two identical massless springs A and B and a block of mass 2kg is hanging with a third identical spring C as shown in figure then the magnitude of acceleration of 3kg and 2kg block just after cutting the spring A DA 25 3 B 5363 50 50 8 mmmmmm 3kg C 2kg 30 m 8 and zero m s and zero m s 10 m s D 20 m s zero m s

A machine gun is mounted on a 2800 kg vehicle on a horizontal smooth rod negligible friction The gun fires 10 bullets per sec with a velocity of 200 m s If the mass of each bullet is 50 g What is the acceleration produced in the vehicle a 3 5 cm s c 5 2 cm s b 4 cm s d 4 9 cm s

A heavy particle hanging from a string of length is projected horizontally with speed g in a vertical plane The speed of the particle at the point where the tension in the string equals to weight of the particle is gr ted m s Find K

mass 1 kg is released rom rest which can move along the rod as shown At the release point spring is vertical and relaxed The natural length of the spring is 3 1 m g 10 m s Rod makes an angle of 30 with the horizontal Ring again comes to rest when spring makes an angle of 30 with the vertical Immmmmm 30 A Force constant of the spring is 3 1 N m B Maximum displacement of ring is 2 3 1m C Maximum extension in the spring is 3 1 m D Normal reaction on ring due to rod when it again comes to rest is

Zero Marks In all other cases A solid sphere of mass m 2 kg and specific gravity S 0 5 is held stationary relative to tank filled with water The tank is accelerating upward with acceleration 2 m s The tension in the string in found to be 8 n Find the value of n Given density of water 1000 kg m and g 10 m s a 2m s

A rectangular container is accelerated horizontally Water is filled upto a height of 2m in this containers having dimensions 5m x 4 3m ao 3m 5 m s2 Water 5m Find maximum acceleration that can be given without spilling the water O 4 m s O 3 m s 2m

A fixed pulley of radius 20 cm and moment of inertia 0 32 kg m about its axle has a massless cord wrapped around its rim A mass M 2 kg is attached to the end of the cord The pulley can rotate about its axis without any friction The acceleration of the mass M Assume g 10 m s 1 m s O 3 m s O 2 m s 4 m s M

A plane mirror reflecting a ray is rotated through an angle about an axis through the point of incidence in the plane the mirror perpendicular to the plane of incidence then 1 The reflected ray does not rotate 2 The reflected ray rotates through an angle 0 3 The reflected ray rotates through an angle 20 4 The incident ray rotates through an angle A

In the given figure mass of block A is m and that B is 2m They are attached at the ends c spring and kept on horizontal surface Now the spring is compressed by Xo and released Find displacement of block B by the time compression of the spring is reduced to XO 2 Assuem both are slipping in opposite directions together A B 2m m 0 2 0 1

0 a as shown in figure The block is observed by two observers A and B for a time interval t A mg t 2 The observer B finds that the work done by gravity is 1 B mg t c mgat C a D mgat The observer B finds that work done by normal reaction N is A zero Nat 2 B 2 B Nat D None of these

Three blocks A B and C placed on a smooth horizontal surface are being pushed with a force of 60 N as shown below The contact force between block A and B is 30 N an that between block B and C is 10 N The ratio of masses of blocks A B and C is ABC Smooth horizontal surface 60 N TTT

Upper edges of two identical uniform planks each of mass M 87 kg and length 1 1 0 m are hinged to a horizontal axle affixed to the ceiling A cylinder of mass m 20 kg and radius r 0 30 m is inserted horizontally between the planks as shown The cylinder touches the planks at a distance 77 0 75 times the length of the plank from the hinge Find range of coefficient of friction between the planks and the cylinder to keep the system in equilibrium s

Electric field in a region of space is radially outward from origin and varies with distance r from origin as E kr Find the charge enclosed in a sphere of radius a centred at origin 1 4k 3 k 2 2k 3 k 4

5 A block of mass m slides on a frictionless inclined plane of mass M which in turn is free to slide on a frictionless horizontal surface Use d Alembert s principle to find the equations of motion of the block and the plane taking as generalized coordinates the displacement s of the block down the plane and the horizontal displacement z of the plane M E a

m L Problem 4 Figure 1 left For this static system find the equation of constrain and the condition for equilibrium using the principal of virtual work Figure 1 right Find the degree s of freedom and the type of constraint Show using the principal of virtual work m ym 2 where y is the coefficient of friction

Figure 1 left For this static system find the equation of constrain and the condition for equilibrium using the principal of virtual work Figure 1 right Find the degree s of freedom and the type of constraint Show using the principal of virtual work m ym 2 where y is the coefficient of friction

Three blocks with masses 6 0 kg 9 0 kg and 10 kg are connected as shown in Fig 3 23 The coeff friction between the table and the 10 kg block is 0 20 Find a the acceleration of the system and tension in the cord on the left and in the cord on the right Ans a 0 39 m s b 61 85 P P 6 0 kgl M 0 20 10 kg